Define a Set $S$ Recursively as Follows:
I $11 \in S$ II RECURSION:
A

question 31

Essay

Define a set $S$ recursively as follows:
I. BASIS: $11 \in S$
II. RECURSION:
a. If $s \in S$ , then $0 s \in S$ and $s 0 \in S$
b. If $x$ is any string (including the null string) such that $1 x 1 \in S$ , then $10 x 1 \in S$ and $1 x 01 \in S$ III. RESTRICTION: No strings other than those derived from I and II are in $S$ .
a. Is $010010 \in S$ ? Justify your answer.
b. Is $011011 \in S$ ? Justify your answer.

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Definitions:

T Score

A standardized score with a mean of 50 and a standard deviation of 10, often used in psychological and educational testing to compare an individual's test performance with a norm group.

Test-Retest Reliability

Giving the test twice to the same group of people and then correlating the scores of the first test with those of the second test to determine the reliability of the instrument.

Sten

A standard ten scale used for scoring and interpreting psychological and other types of tests, where scores are often transformed to fit a scale ranging from 1 to 10.

DIQ

An abbreviation often used for Differential Intelligence Quotient, though not commonly recognized in standard intelligence testing terminology.